This paper investigates the issues related to the cell assembly delay induced by filling AAL2 packets from different users into the payloads of ATM cells. A conclusion is drawn that the cell assembly delay is affected by the voice coding rate, voice packetization interval and the number of voice sources multiplexed. When the number of voice sources multiplexed is small and voice is compressed to a low bit rate, a timer is needed to limit the cell assembly delay. Timer can be set at 3ms if voice is compressed using 8kb/s G.729. When voice is compressed using 32kb/s G.726 with a voice packetization interval of 5ms, it is unnecessary to use the timer.